1. Field of the Invention
The present invention relates to digital signal processing; and more particularly, to machines and methods for determining characteristics of signals having frequency components that vary in time.
2. Description of the Related Art
Typical systems for digital signal processing involve conversion of an input analog signal to a sequence of digital samples, supplying blocks of the digital samples in the sequence to a digital signal processing engine which performs array or block level computations on the digital signals, and analyzing the results of the computations. This field is rapidly expanding in the areas of speech processing, image recognition for radar and sonar, underwater acoustics, and other technologies.
The discrete Fourier transform DFT and fast Fourier transform FFT implementation of the DFT, are fundamental processing techniques in digital signal processing systems. These techniques suffer the limitation that they do not characterize signals being processed in terms of how frequency components vary in time very well.
Prior art systems for analyzing signals with frequency components that vary in time have used the so-called short time Fourier transform STFT. This algorithm is based on a computationally intensive Fourier transform of a large number of short windows of the input signal. Transforms of each of the short time windows are combined to generate a time varying spectrum of the input signal. However, time varying spectra generated using the STFT technique do not have very good resolution. Also, the STFT technique is computationally expensive.
The Gabor transform is another digital signal processing tool which generates a joint time-frequency representation of a signal. See, D. Gabor, "Theory of Communication", J.IEE (London), Vol. 93, No. III, November, 1946, pp. 429-457. Its applications, however, have been limited primarily due to the difficulty of selecting the biorthogonal auxiliary window function .gamma.. Recently, a framework for designing the auxiliary function .gamma. for the finite and cyclic discrete Gabor transform has been developed. See, Wexler, et al., "Discrete Gabor Expansions", Signal Processing, Vol. 21, No. 3, November, 1990, pp. 207-221. In many signal processing applications, however, the finite, cyclic Gabor transform is not adequate. The lack of a general solution for the infinite discrete Gabor transform has limited the usefulness of this digital processing technique, and it has not been applied successfully to creating time-varying energy spectra. See, Qian, et al., "Wigner Distribution Decomposition and Cross-Term Interference Cancellation", UMBC Technical Report No. EER-91-1, University of Maryland, January, 1991.